I would suggest that you know how to complete the following simple mechanical tasks:

1) Patch or replace a flat inner tube
2) "Boot" a torn tire
3) Fix a broken chain
4) Fix a broken spoke
5) True an out of round wheel
6) Lube the chain
7) Replace a broken brake or shift cable
8) Replace worn brake pads
9) Tighten any loose bolt
10) Adjust the shifting of front and rear derailleurs
11) Adjust the position of brake and shift levers
12) Adjust the position of the stem and handlebars

This isn't to say that you have to carry the tools or parts to do all of these things on the side of the road, however. I know how to replace my brake pads, for instance, but that doesn't mean I travel with a spare set of pads: if I see that the pads are getting bad, I'll buy some when I pass a bike shop then replace them at my leisure. I know how to do the work, so I'm not stuck waiting for help from a shop mechanic.